Question

已知：函数f(x)=2cosx+(sinx)^2,-45°

Answer 1

f(x)=2cosx+(sinx)^2=2cosx+1-(cosx)^2

= -(cosx)^2+2cosx+1 (-π/4,π/2]

令：t=cosx

因为 (-π/4,π/2],所以 [0,1]

原式为：

f(t)= -t^2+2t+1 [0,1]

f(t)= -t^2+2t+1

= -(t-1)^2+2

结合定义域可知,当t=0时,取最小值.

f(t)min=f(0)=1

t=cosx=0 ------------------x=π/2